References
- Bordag , L.A. 2008 . “ On option-valuation in illiquid markets: invariant solutions to a nonlinear model ” . In Proceedings of Workshop on Mathematical Control Theory and Finance , Mathematical Control Theory and Finance Edited by: Sarychev , A. , Shiryaev , A. , Guerra , M. and Grossinho , M.R. 71 – 94 . Springer . April 10–14, 2007 CL Lisabon, PORTUGAL
- Bordag , L.A. 2008 . Symmetry reductions and exact solutions for nonlinear diffusion equations . Int. J. Mod. Phys. A , 24 ( 8–9 ) : 1713 – 1716 .
- Bordag , L.A. 2010 . Pricing options in illiquid markets: optimal systems, symmetry reductions and exact solutions . Lobachevskii J. Math. (LJM) , 31 ( 1 ) : 90 – 99 .
- Bordag , L.A. and Frey , R. 2009 . “ Pricing options in illiquid markets: symmetry reductions and exact solutions ” . 103 – 130 . New York : Nova Science Publishers, Inc. . chapter 3 in the book Nonlinear Models in Mathematical Finance: Research Trends in Option Pricing
- Frey , R. 1998 . Perfect option replication for a large trader . Finance Stochastics , 2 : 115 – 148 .
- Hoggardt , T. , Whalley , A.E. and Wilmott , P. 1994 . Hedging option portfolios in the presence of transaction costs . Adv. Futures Options Res. , 7 : 21 – 35 .
- Ibragimov , N.H. 1999 . Elementary Lie Group Analysis and Ordiary Differential Equations , Chichester, USA : John Wiley & Sons .
- Jandačka , M. and Ševčovič , D. 2005 . On the risk-adjusted pricing-methodology-based valuation of vanilla options and explanation of the volatility smile . J. Appl. Math. , 3 : 253 – 258 .
- Kabanov , Yu.M. and Safarian , M.M. 1997 . On Leland's strategy of option pricing with transaction costs . Finance Stochast. , 1 : 239 – 250 .
- Kabanov , Yu.M. and Safarian , M.M. 2010 . Marktes with transaction costs , Berlin, Heidelberg : Springer . Mathematical Theory, Series: Springer Finance
- Kratka , M. 1998 . No mystery behind the smile . Risk , 9 : 67 – 71 .
- Kwok , Y.K. 1998 . Mathematical Models of Financial Derivatives , Springer .
- Leland , H.E. 1985 . Option pricing and replication with transaction costs . J. Finance , 40 : 1283 – 1301 .
- Leland , H.E. 2007 . Comments on “Hedging errors with Leland's option model in the presence of transaction costs” . Finance Res. Lett. , 4 : 200 – 202 .
- Olver , P.J. 1986 . Application of lie groups to differential equations , New York : Springer .
- Ovsiannikov , L.V. 1982 . Group analysis of differential equations , New York : Academic Press .
- Patera , J. and Winternitzs , P. 1977 . Subalgebras of real three- and four-dimensional Lie algebras . J. Math. Phys. , 18 ( 7 ) : 1449 – 1455 .
- Ševčovič , D. 2009 . Transformation methods for evaluating approximations to the optimal exercise boundary for linear and nonlinear Black–Scholes equations , 173 – 218 . New York : Nova Science Publishers, Inc. . chapter 6 in the book Nonlinear Models in Mathematical Finance: Research Trends in Option Pricing
- Sircar , R. and Papanicolaou , G. 1998 . General Black–Scholes models accounting for increased market volatility from hedging strategies . Appl. Math. Finance , 5 : 45 – 82 .